1. Mc PRESENT WORTH ANALYSIS Graw Hill CHAPTER V
ENGINEERING ECONOMY Fifth Edition Mc
Graw
Hill
Blank and Tarquin
CHAPTER V
PRESENT WORTH ANALYSIS
Adopted and modified by Dr. W-.W. Li of UTEP, Fall, 2003
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

2. 5.1 FORMULATING MUTUALLY EXCLUSIVE ALTERNATIVES
Mutually Exclusive set is where a candidate set of alternatives exist (more than one)
Objective: Pick one and only one from the set.
Once selected, the remaining alternatives are excluded.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

3. 5.1 INDEPENDENT PROJECT SET
Given a set of alternatives (more than one)
The objective is to:
Select the best possible combination of projects from the set that will optimize a given criteria.
Subjects to constraints
More difficult problem than the mutually exclusive approach
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

4. 5.1 FORMULATING MUTUALLY EXCLUSIVE ALTERNATIVES
Mutually exclusive alternatives compete with each other.
Independent alternatives may or may not compete with each other
The independent project selection problem deals with constraints and may require a mathematical programming or bundling technique to evaluate.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

5. Service – the alternatives consist mainly of cost elements
5.1 Type of Alternatives
Revenue/Cost – the alternatives consist of cash inflow and cash outflows
Select the alternative with the maximum economic value
Service – the alternatives consist mainly of cost elements
Select the alternative with the minimum economic value (min. cost alternative)
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

6. 5.1 Evaluating Alternatives
In part, the role of the engineer to properly evaluate alternatives from a technical and economic view
Must generate a set of feasible alternatives to solve a specific problem/concern
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

7. 5.1 Alternatives Analysis Selection Problem Execution Do Nothing Alt.2
Problem
Alt. m
Execution
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

8. 5.2 Present Worth Approach
A process of obtaining the equivalent worth of future cash flows to some point in time
– called the Present Worth
At an interest rate usually equal to or greater than the Organization’s established MARR.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

9. 5.2 THE PRESENT WORTH METHOD
P(i%) = P( + cash flows) + P( - cash flows)
If P(i%) > 0 then the project is deemed acceptable.
If P(i%) < 0 – the project is usually rejected
If P(i%) = 0 Present worth of costs = Present worth of revenues: Indifferent!
Note: If the present worth of a project turns out to = “0,” that means the project earned exactly the discount rate that was used to discount the cash flows! The interest rate that causes a cash flow’s NPV to equal “0” is called the Rate of Return of the cash flow!
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

10. 5.2 PRESENT WORTH: Special Applications
Present Worth of Equal Lived Alternatives
Alternatives with unequal lives: Beware
Capitalized Cost Analysis
Require knowledge of the discount rate before we conduct the analysis
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

11. 5.2 PRESENT WORTH: Equal Lives
Present Worth of Equal Lived Alternatives – straightforward
Compute the Present Worth of each alternative and select the best, i.e., smallest if cost and largest if profit.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

12. 5.2 PRESENT WORTH: Example
Consider: Machine A Machine B
First Cost $2,500 $3,500
Annual Operating Cost
Salvage Value
Life 5 years 5 years
i = 10% per year
Which alternative should we select?
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

13. 5.2 PRESENT WORTH: Cash Flow Diagram
$2,500
A = $900
F5=$200 MA
$3,500
F5=$350
A = $700 MB
Which alternative should we select?
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

14. 5.2 PRESENT WORTH: Solving
PA =-2, (P|A, .10, 5) +
200 (P|F, .01, 5)
=-2, (3.7908) (.6209)
= -2, , = -$5,788
PB = -3, (P|A, .10, 5) +
350 (P|F, .10, 5)
= -3, , = -$5,936
SELECT MACHINE A: Lower PW cost!
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

15. 5.3 PRESENT WORTH: Different Lives
Comparison must be made over equal time periods
Compare over the least common multiple, LCM, for their lives
Note: if the lives of the alternatives are not equal, one must create or force a study period where the life is the same for all of the alternatives. One cannot effectively compare the PW of one alternative with a study period different from another alternative that does not have the same study period.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

16. 5.3 PRESENT WORTH: Lowest Common Multiple of Lives
If the alternatives have different study periods, you find the lowest common life for all of the alternatives in question.
Example: {3,4, and 6} years. The lowest common life is 12 years.
Evaluate all over 12 years for a PW analysis.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

17. 5.3 PRESENT WORTH: Example Unequal Lives
Machine A Machine B
First Cost $11,000 $18,000
Annual Operating Cost 3, ,100
Salvage Value , ,000
Life 6 years 9 years
i = 15% per year
Note: Where costs dominate a problem it is customary to assign a positive value to cost and negative to inflows
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

18. 5.3 PRESENT WORTH: Unequal Lives
$11,000
F6=$1,000
A 1-6 =$3,500
Machine A
F6=$2,000
A 1-9 =$3,100
$18,000
Machine B
i = 15% per year
LCM(6,9) = 18 year study period will apply for present worth
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

19. 5.3 Unequal Lives: 2 Alternatives
Machine A
Cycle 1 for A
Cycle 2 for A
Cycle 3 for A
6 years
Machine B
Cycle 1 for B
Cycle 2 for B
18 years
9 years
i = 15% per year
LCM(6,9) = 18 year study period will apply for present worth
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

20. 5.3 Example: Unequal Lives Solving
LCM = 18 years
Calculate the present worth of a 6-year cycle for A
PA = -11, ,500 (P|A, .15, 6) +
1,000 (P|F, .15, 6)
= -1, ,500 (3.7845) + 1,000 (.4323)
= -$23,813, which occurs at time 0, 6 and 12
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

21. 5.3 Example: Unequal Lives
Machine A
$23,813
PA= -23,813-23,813 (P|F, .15, 6)-
23,813 (P|F, .15, 12)
= -23, , ,451 = -$38,558
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

22. 5.3 Unequal Lives Example: Machine B
Calculate the Present Worth of a 9-year cycle for B
F6=$2,000
A 1-9 =$3,100
$18,000
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

23. 5.3 9-Year Cycle for B
Calculate the Present Worth of a 9-year cycle for B
PB = -18,000-3,100(P|A, .15, 9) +
2,000(P|F, .15, 9)
= -18, ,100(4.7716) + 2,000(.2843)
= -$33,359 which occurs at time 0 and 9
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

24. 5.3 Alternative B – 2 Cycles
Machine A: PW =$38,558
$32,508
PB = -32, ,508 (P|F, .15, 9)
= -32, ,508(.2843)
PB = -$41,750
Choose Machine A
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

25. 5.3 Unequal Lives – Assumed Study Period
Study Period Approach
Assume alternative: 1 with a 5-year life
Alternative: 2 with a 7-year life
Alt-1: N = 5 yrs
LCM = 35 yrs
Alt-2: N= 7 yrs
Could assume a study period of, say, 5 years.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

26. 5.3 Unequal Lives – Assumed Study Period
Assume a 5-yr. Study period
Estimate a salvage value for the 7-year project at the end of t = 5
Truncate the 7-yr project to 5 years
Alt-1: N = 5 yrs
Now, evaluate both over 5 years using the PW method!
Alt-2: N= 7 yrs
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

27. FW(i%) is an extension of the present worth method
5.4 FUTURE WORTH APPROACH
FW(i%) is an extension of the present worth method
Compound all cash flows forward in time to some specified time period using (F/P), (F/A),… factors or,
Given P, the F = P(1+i)N
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

28. 5.4 Applications of Future Worth
Projects that do not come on line until the end of the investment period
Commercial Buildings
Marine Vessels
Power Generation Facilities
Public Works Projects
Key – long time periods involving construction activities
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

29. 5.4 Future Worth Example (Figure 5.3)
See Example 5.3
Calculate the Future Worth of determining the selling price in order to earn exactly 25% on the investment
Draw the cash-flow diagram!!
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

30. CAPITALIZED COST- the present worth of a project that lasts forever.
Government Projects
Roads, Dams, Bridges (projects that possess perpetual life)
Infinite analysis period
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

31. 5.5 Derivation for Capitalized Cost
Start with the closed form for the P/A factor
Next, let N approach infinity
Or, CC(i%) = A/i
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

32. 5.5 CAPITALIZED COST
Assume you are called on to maintain a cemetery site forever if the interest rate = 4% and $50/year is required to maintain the site.
N=inf.
A=$50/yr
P = ?
…………………..
Find the PW of an infinite annuity flow
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

33. P0=A(1/i) 5.5 CAPITALIZED COST ………………….. P = ? P0 = A[P/A,i%,N]
N=inf.
A=$50/yr
P = ?
Find the PW of an infinite annuity flow
…………………..
P0=A(1/i)
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

34. 5.5 CAPITALIZED COST
P0 = $50[1/0.04]
P0 = $50[25] = $1,250.00
Invest $1,250 into an account that earns 4% per year will yield $50 of interest forever if the fund is not touched and the i-rate stays constant.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

35. 5.5 CAPITALIZED COST: Endowments
Assume a wealthy donor wants to endow a chair in an engineering department.
The fund should supply the department with $200,000 per year for a deserving faculty member.
How much will the donor have to come up with to fund this chair if the interest rate = 8%/yr.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

36. 5.5 CAPITALIZED COST: Endowed Chair
The department needs $200,000 per year.
P = $200,000/0.08 = $2,500,000
If $2,500,000 is invested at 8% then the interest per year = $200,000
The $200,000 is transferred to the department, but the principal sum stays in the investment to continue to generate the required $200,000
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

37. EXAMPLE 5.5 Capitalized Cost Example
Calculate the Capitalized Cost of a project that has an initial cost of $150,000. The annual operating cost is $8,000 for the first 4 years and $5000 thereafter. There is an recurring $15,000 maintenance cost each 15 years. Interest is 15% per year.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

38. 5.5 Cash Flow Diagram
“i”=15%/YR
$4,000
………
$150,000
$8,000
$15,000
N=
How much $$ at t = 0 is required to fund this project?
The capitalized cost is the total amount of $ at t = 0, when invested at the interest rate, will provide annual interest that covers the future needs of the project.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

39. 5.5 CAPITALIZED COST - Example Continued
1. Consider $4,000 of the $8,000 cost for the first four years to be a one-time cost, leaving a $4,000 annual operating cost forever.
P0= 150, ,000 (P|A, .15, 4) = $161,420
2.855
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

40. 5.5 CAPITALIZED COST - Continued
Recurring annual cost is $4,000 plus the equivalent annual of the 15,000 end-of-cycle cost.
…….
……..
Take any 15-year period and find the equivalent annuity for that period using the F/A factor.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

41. 5.5 CAPITALIZED COST: One Cycle
Take any 15-year period and find the equivalent annuity for that period using the F/A factor
……..
…….
$15,000
A for a 15-year period
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

42. Recurring costs = -$4,315/i = -4,315/0.15 =-$28,767/yr
5.5 CAPITALIZED COST
2. Recurring annual cost is $4,000 plus the equivalent annual of the 15,000 end-of-cycle cost.
A= -4, ,000 (A|F, .15, 15)
= -4, (.0210) = -$4,315
Recurring costs = -$4,315/i = -4,315/0.15 =-$28,767/yr
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

43. 5.5 CAPITALIZED COST Capitalized Cost = 161,420 + 5315/.15 = $196,853
Thus, if one invests $196,853 at time t = 0, then the interest at 15% will supply the end-of-year cash flow to fund the project so long as the principal sum is not reduced or the interest rate changes (drops).
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

44. 5.6 Payback Period Analysis
Two forms for this method
Discounted Payback Period (uses an interest rate)
Conventional Payback Period (does not use an interest rate)
Payback is the period of time it takes for the cash flows to recover the initial investment.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

45. 5.6 Payback Period Analysis
Discounted Payback Approach
Find the value of np such that:
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

46. 5.6 Payback for Example 5.8 Discounted Undiscounted
Machine A: 6.57 years
Machine B: 9.52 years
Undiscounted
Machine A: 4.0 years
Machine B: 6.0 years
Go with Machine A – lower time period payback to recover the original investment
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

47. 5.6 Payback Method Summarized
Payback is only a rough estimator of desirability
Use as an initial screening method
Avoid using this method as a primary analysis technique for selection projects
Totally avoid the no-return payback period
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

48. Extension of the Present Worth method
5.7 Life Cycle Costs (LCC)
Extension of the Present Worth method
Used for projects over their entire life span where cost estimates are employed
Used for:
Military/Defense Projects
New Product Lines
Large construction projects
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

49. 5.7 Life Cycle Defined – Detailed Phases
Needs Assessment Phase
Conceptual Design Phase
Detailed Design Phase
Production/Construction Phase
Operation – (upgrading to extend) Phase
Retirement/Disposal Phase
The life can be for years into the future
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

50. 5.7 Life Cycle: Two General Phases
TIME
Cost-$
Cumulative Life Cycle Costs
Acquisition Phase
Operation Phase
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

51. 5.7 Life-Cycle Costs: Impact of Design Changes
Cost of a design change tends to multiply by 10 with each phase
Any design changes that might occur late in the life cycle drastically increase the total life cycle costs!
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

52. 5.7 Life-Cycle Costs: Acquisition Phase
Rule: About 80% of LCC are locked in by the end of the Acquisition Phase.
Emphasis is on good design!
Costs - $
Needs Assessment
Conceptual Design
Detailed Design
Acquisition Phase
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

53. 5.7 Life-Cycle Costs – Purpose
Make explicit as possible the relationship of costs over the total life span of a product/system
Design Process Objective
Minimize the life-cycle costs
And meet other performance requirements
By making correct trade-offs between costs in the acquisition phase and costs during the operations phase
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

54. 5.7 Life-Cycle Costs – Warning
Beware of introducing certain cost- cutting measures in the acquisition phase and early production phase
Such cost-cutting measures could impact the future operations and degrade safety or require modifications later on
These cost-cutting measures can be misleading and dangerous!
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

55. 5.7 Life-Cycle Costs – Warning
Engineers have a ethical and moral responsibility to ensure that designs are:
Economically sound
Functional
Safe
Perform as expected
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

56. Bonds represent a source of funds for the firm.
5.8 Present Worth of Bonds
Bonds represent a source of funds for the firm.
Bonds are sold (floated) by investment banks for firms in order to raise additional debt capital
A bond is similar to an IOU
Bonds are evidence of Debt
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

57. 5.8 Bond Types – Treasury Bonds
Issued by Federal Government
Full backing of the Government
1 year or less; 2-10 year issues; and year issues
Conservative-type investment
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

58. 5.8 Bond Types – Municipal Bonds
State and Municipal Bonds
Issued by states and local governments
Generally tax-exempt by the Federal Government
Used to finance state and local projects
Backed by future tax and user fees to pay the interest and face value
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

59. 5.8 Bond Types – Mortgage Bonds
Issued by Corporations
Secured by the firm’s assets
Money received by the firm is used to fund projects
Referred to a Debt Capital
Buyers of these bonds are not owners – they are lenders to the firm
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

60. 5.8 Bond Types – Debentures
Debenture Bond
Issued by Corporations
Not backed by specific assets
Backing – good faith of the firm
Pays higher interest rates
Higher risks involved
Bond interest rate may “float”
Could be convertible to common stock
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

61. 5.8 Present Worth of Bonds – Overview
Investment Bankers
The Firm
Commissions/Fees
Sell the Bonds to
The lending public
Proceeds from
The sale
Bondholders
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

62. Bonds are negotiable instruments
5.8 Bonds – Basics
Bonds are negotiable instruments
Can be traded by the current bondholder
Source of funds to the firm
Debt capital
Bondholders are loaning $$ to the firm
Earn periodic interest
Sell the bonds at any time
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

63. Firm authorizes a bond sale Bonds are sold by an outside agency
5.8 Bonds – Firm’s View
Firm authorizes a bond sale
Bonds are sold by an outside agency
Firm pays a commission to the selling agency
The firm receives the proceeds from the sale
This is now DEBT capital to the firm
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

64. 5.8 Bond Basics – Continued
The bondholders are not owners
They are lendors
The firm pays periodic interest payments to the current bond holders
At the end of the bond’s life, the bonds are redeemed (bought back) from the current bond holder
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

65. 5.8 Bond Basics - Continued
The bond itself is just a piece of paper
Evidence of the debt the firm has incurred
The firm may be able to “call” the bonds back by paying the current bondholder a calculated sum
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

66. V – The face value of the bond
5.8 Bonds – Notation
P0 – The time t = 0 selling price of the bond – the cost to the buyer of the bond
V – The face value of the bond
The value printed on the bond
Face values are usually:
$100, $1,000, $5,000, $10,000 increments
N – The life of the bond in years
r – The nominal annual bond interest rate
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

67. 5.8 Bonds – Notation and Example
Given the nominal annual bond interest rate, the payment frequency of the interest (monthly, quarterly semi-annually, etc.) is also stated
Example:
V = $5,000 (face value)
r = 4.5% per year paid semiannually
N = 10 years
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

68. 5.8 Bonds – Example – Continued
The interest the firm would pay to the current bondholder is calculated as:
The bondholder, buys the bond and will receive $ every 6 months for the life of the bond
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

69. 5.8 Bonds – Example 5.11 Given V = $10,000 (Face value of the bond)
r = 4.5% paid semiannually
N = 10 years or 20 interest periods
$I/6 months = $5,000(0.045/2) = $ paid to the current bondholder
Bonds are bought at sold in a bond market. Thus the price of the bond is subject to the pressures of the bond market.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

70. 5.8 Example 5.11
Key Point – The purchase price of the bond can be considered a value that is determined by a willing buyer and a willing seller.
Assume the potential buyer of this bond requires a interest rate of no less than 8%/year compounded quarterly.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

71. The purchaser will consider this bond if he/she can earn 8%/yr c.q.
5.8 Example 5.11 – Continued
The purchaser will consider this bond if he/she can earn 8%/yr c.q.
What is fixed?
The future interest payments are fixed
The future face value of the bond in fixed
What can vary?
The purchase price such that the buyer can earn at least the 8%/yr c.q.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

72. 8% c.q is the same as 5.8 Example 5.11 – Continued
0.08/4 = 0.02 = 2% per quarter.
Bond interest flows every 6 months
Need an effective 6-month rate
The effective 6-month rate is then
(1.02)2 – 1 – = 4.04%/6 months
This is the potential buyer’s required interest rate
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

73. Draw the cash-flow diagram Work the problem with N = 20 (not 10)
5.8 Example 5.11 – Solving
The objective is to determine the purchase price of this bond discounted at the buyer’s required rate of 4.04% per 6 months
Draw the cash-flow diagram
Work the problem with N = 20 (not 10)
We have 20 interest payments (every 6 months) = 10 years
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

74. 5.8 Example 5.11 – Cash-Flow Diagram
… …
P=??
$5,000
i=4.04%/6 months
A = /6 months
Find the PW(4.04%) of the future cash flows to the potential bond buyer
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

75. 5.8 Example 5.11 – Solving P = $112.50(P/A,4.04%,20)
+ $5,000(P/F,2%,40)
P = $3,788
IF the buyer can buy this bond for $3,788 or less, he/she will earn at least the 8% c.q. rate.
Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.